Martingales and reliability theory: marked point signatures processes
| Full text | |
| Author(s): |
Fagundes, Pedro
;
Koshlukov, Plamen
Total Authors: 2
|
| Document type: | Journal article |
| Source: | Linear Algebra and its Applications; v. 677, p. 21-pg., 2023-08-28. |
| Abstract | |
Let A = B + C be an associative algebra graded by a group G, which is a sum of two homogeneous subalgebras B and C. We prove that if B is an ideal of A, and both B and C satisfy graded polynomials identities, then the same happens for the algebra A. We also introduce the notion of graded semi-identity for the algebra A graded by a finite group and we give sufficient conditions on such semi-identities in order to obtain the existence of graded identities on A. We also provide an example where both subalgebras B and C satisfy graded identities while A = B+C does not. Thus the theorem proved by K,epczyk in 2016 does not transfer to the case of group graded associative algebras. A variation of our example shows that a similar statement holds in the case of group graded Lie algebras. We note that there is no known analogue of K,epczyk's theorem for Lie algebras. (AU) | |
| FAPESP's process: | 22/05256-2 - Images of multilinear polynomials on UT_2 and UT_3 with involutions |
| Grantee: | Pedro Souza Fagundes |
| Support Opportunities: | Scholarships abroad - Research Internship - Doctorate |
| FAPESP's process: | 19/16994-1 - Algebras that are sums of two PI subalgebras |
| Grantee: | Pedro Souza Fagundes |
| Support Opportunities: | Scholarships in Brazil - Doctorate |
| FAPESP's process: | 18/23690-6 - Structures, representations, and applications of algebraic systems |
| Grantee: | Ivan Chestakov |
| Support Opportunities: | Research Projects - Thematic Grants |